cusp

1. (figuratively) An important moment when a decision is made that will determine future events.Examples: "Newcastle were 11 points adrift of Spurs following their 5-0 mauling at the hands of the north London club in February. But a sixth successive Premier League win puts them on the cusp of European football next season as they surged 15 points clear of seventh-placed Everton, who have five games left to play."figuratively

2. (geometry) A point of a curve where the curve is continuous but has no derivative, but such that it has a derivative at every nearby point.

3. (architecture) A point made by the intersection of two curved lines or curved structures, a common motif in Gothic architecture.

4. (astrology) A boundary between zodiacal signs and houses.

5. (dentistry) Any of the pointed parts of a canine tooth or molar.

6. (anatomy) A flap of a valve of a heart or blood vessel.